Problem: Simplify the following expression: $k = \dfrac{5qr + r}{2pr + 2r^2} - \dfrac{r^2 - 5qr}{2pr + 2r^2}$ You can assume $p,q,r \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{5qr + r - (r^2 - 5qr)}{2pr + 2r^2}$ $k = \dfrac{10qr + r - r^2}{2pr + 2r^2}$ The numerator and denominator have a common factor of $r$, so we can simplify $k = \dfrac{10q + 1 - r}{2p + 2r}$